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garri49 [273]
3 years ago
11

- 16(x - 2)² – 25=0​

Mathematics
1 answer:
Amanda [17]3 years ago
8 0

Answer:

x=2±16i\sqrt{73}

Step-by-step explanation:

1.) Using the PEMDAS distribute the (x-2)^{2} using the FOIL method

(x-2)^2= x^2-4x+4

2.) Distribute the -16 to ((x-2)^2= x^2-4x+4)

-16(x^2-4x+4)= -16x^2+64x-64

3.) Add the -25 to the equation

(-16x^2+64x-64)-25=-16x^2+64x-89=0

4.) Since this isn't factor-able, you must use the quadratic formula,

\frac{(-b (+ or -) \sqrt{(b^2-4ac)}}{2a} and distrubute the numbers

a=-16 b=64 and c=-89

5.) Simplify the radical by finding the factors of -18688 that has a perfect root as one of the factors (which is -256 and 73).

\sqrt{-18688} =\sqrt{-256*73} =16i\sqrt{73}

6.)Simplify the fraction

\frac{-64(+ or -)16i\sqrt{73} }{-32} ={2}(+ or -)16i\sqrt{73}

7.) Your two roots are:

{2}(+ or -)16i\sqrt{73}

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Answer:

The company will expect to replace 13.03% of batteries.

The company should guarantee the batteries for 35 months.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 45, \sigma = 8

If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{36 - 45}{8}

Z = -1.125

Z = -1.125 has a pvalue of 0.1303.

The company will expect to replace 13.03% of batteries.

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries

They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

Z = \frac{X - \mu}{\sigma}

-1.28 = \frac{X - 45}{8}

X - 45 = -1.28*8

X = 34.76

Rounding to the nearest month

The company should guarantee the batteries for 35 months.

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3 years ago
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